Thanks for all the input guys!
I think my question comes down to the idea of putting a skimmer BELOW the water line, which as far as I can tell is not going to work, given that the bullet 2 is open to the atmosphere. If anyone has tried this, please let me know! I am pretty sure that as long as you had a pump that was powerful enough, you could put a beckett style skimmer as high as you wanted... but the point is that I would like lots of volume in my sump, in addition to keeping the space it occupies to a minimum. Here's what I have on my drawing board so far:
So as you can see, clearance is going to be an issue. I think that I can raise the skimmer a bit and still be ok all around. I'll post the new sump plan when it's finished.